Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method
Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method
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DOI：
10.1016/j.jfa.2019.108339
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发表时间：
2018-04
影响因子：
1.7
通讯作者：
E. Grenier;Toan T. Nguyen;F. Rousset;A. Soffer
中科院分区：
文献类型：
--
作者：
E. Grenier;Toan T. Nguyen;F. Rousset;A. Soffer
本文研究了无界通道T× R中混合层剪切流的二维Euler和Navier-Stokes方程线性化解的大时间行为。在一个简单的自伴算子谱稳定性假设下，我们证明了线性无粘阻尼的局部形式是一致的小粘度。我们还证明了在ν− 1/3阶时发生的局部形式的粘性耗散增强，其中ν是小粘性。为了证明这些结果，我们使用哈密顿方法，以下共轭算子的薛定谔算子的研究中开发的方法，结合hypoverravity参数来处理粘性的情况。
We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel T× R. Under a simple spectral stability assumption on a self-adjoint operator, we prove a local form of the linear inviscid damping that is uniform with respect to small viscosity. We also prove a local form of the enhanced viscous dissipation that takes place at times of order ν− 1/3, ν being the small viscosity. To prove these results, we use a Hamiltonian approach, following the conjugate operator method developed in the study of Schrödinger operators, combined with a hypocoercivity argument to handle the viscous case.